6.3 Line Spectra and the Bohr
Model
Line Spectra
•
Radiation composed of only one wavelength is called monochromatic.
• Radiation that spans a whole array of different wavelengths is called continuous.
• When radiation from a light source such as a light bulb is separated
into its different wavelength components, a spectrum is produced.
• White light can be separated into a continuous spectrum of colors.
• A rainbow is a continuous spectrum of light produced by dispersal of sunlight by raindrops
or mist.
•
Note that there are no dark spots on the continuous spectrum which would correspond to different lines.
•
Not all radiation is continuous.
•
A gas placed in a partially evacuated tube and subjected to a high voltage produces single colors of light.
•
The spectrum that we see contains radiation of only specific wavelengths; this is called a line spectrum.
Bohr’s Model
•
Rutherford
assumed the electrons orbited the nucleus analogous to planets around the sun.
• However, a charged particle moving in a circular
path should lose energy.
• This means that the atom should be unstable according
to Rutherford’s theory.
• Bohr noted the line spectra of certain elements and assumed the electrons were confined
to specific energy states. These were called orbits.
•
Bohr model is based on three postulates:
•
Only orbits of specific radii, corresponding to certain definite energies, are permitted for electrons in an atom.
• An electron in a permitted orbit has a specific energy and is an "allowed" energy state.
•
Energy is only emitted or absorbed by an electron as it moves from one allowed energy state to another.
• The energy is gained or lost as a photon.
The Energy States of the Hydrogen
Atom
•
Colors from excited gases arise because electrons move between energy states in the atom.
• Since the energy states are quantized, the light emitted from excited atoms must be quantized
and appear as line spectra.
•
Bohr showed mathematically that
•
where n is the principal quantum
number (i.e., n = 1, 2, 3, …. ¼),
and RH is the Rydberg constant = 2.18 x 10–18 J.
•
The first orbit in the Bohr model has n = 1 and is closest to the nucleus.
•
The furthest orbit in the Bohr model has n Ž
¼ and corresponds to E = 0.
• Electrons in the Bohr model can only move between orbits by absorbing
and emitting energy in quanta (E = hn).
• The ground
state = the lowest energy state.
• An electron in a higher energy state is said
to be in an excited state.
•
The amount of energy absorbed or emitted on moving between states is given by
•
When ni > nf
energy is emitted and when nf > ni
energy is absorbed.
Limitations of the Bohr Model
•
The Bohr Model has several limitations:
• It cannot explain the spectra of atoms other
than hydrogen.
• Electrons do not move about the nucleus in circular
orbits.
•
However the model introduces two important ideas:
•
The energy of an electron is quantized: electrons exist only in certain energy levels described by quantum numbers.
• Energy gain or loss is involved in moving an
electron from one energy level to another.
6.4 The Wave Behavior of Matter
•
Knowing that light has a particle nature, it seems reasonable to ask whether matter has a wave nature.
•
This question was answered by Louis deBroglie.
•
Using Einstein’s and Planck’s equations, deBroglie derived:
l
= h/mv
• The momentum, mv, is a particle property, whereas l
is a wave property.
•
Matter waves is the term used to describe wave characteristics of material particles.
•
Therefore, in one equation de Broglie summarized the concepts of waves and particles as they apply to low-mass, high-speed
objects.
•
As a consequence of deBroglie’s discovery, we now have techniques such as X-ray diffraction and electron microscopy
to study small objects.
The Uncertainty Principle
• Heisenberg’s uncertainty principle:
We cannot determine the exact position, direction of motion, and speed of subatomic
particles simultaneously.
•
For electrons: We cannot determine their momentum and position simultaneously.
